A Multi-time Reactive Power Optimization Under Interval Uncertainty of Renewable Power Generation by an Interval Sequential Quadratic Programming Method

Renewable energy sources are a significant means of addressing dwindling conventional fuels and have been increasingly incorporated in transmission power grids on a large scale. However, the uncertainty of renewable energy source power outputs threatens the voltage security of power grids, which restricts the full integration of these sources to some degree. To address this problem, this work employs the reactive power optimization incorporating interval uncertainties (RPOIU) model for the transmission systems. In the RPOIU model, state variables, including load voltages, reactive power generation, and bus angles, are regarded as variables with interval values. Meanwhile, to account for the fluctuation of the load demand and the renewable energy sources in multiple periods of one day, a multi-time RPOIU is proposed. The model seeks to obtain a day-ahead optimal voltage control strategy for ensuring that interval state variables remain within their operating limit constraints in each period of one day, as well for maintaining a low level of daily real power losses. To solve the multi-time RPOIU model, we propose the interval sequential quadratic programming method (ISQPM), which employs a second-order interval Taylor expansion. In addition, an improved interval power flow calculation method, i.e., the optimizing-scenarios method, is employed to obtain the accurate ranges of the interval variables, thus improving the convergence performance of the ISQPM. The quadratic penalty function incorporating the rounding-off process is proposed to deal with the discrete variables in the multi-time RPOIU model. Three cases are tested by simulation to demonstrate the effectiveness, good applicability, and robustness of the proposed method, particularly in comparison to the previously proposed linear approximation method.